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Upper bounds for ruin probabilities in an autoregressive risk model with a Markov chain interest rate
In this paper, ruin probabilities are examined in a discrete time
risk model in which the interest rates follow a Markov chain with a
denumerable state space and the net losses(the claim amount minus
the premium income) are assumed to have a dependent AR(1) structure.
An upper bound for ultimate ruin probability is obtained by
martingale approach. Recursive equations for both finite time ruin
probabilities and ultimate ruin probability are derived. By
integrating the inductive method and the recursive equation, an
upper bound is given for both finite time ruin probabilities and
ultimate ruin probability.